Best Known (137−24, 137, s)-Nets in Base 8
(137−24, 137, 21849)-Net over F8 — Constructive and digital
Digital (113, 137, 21849)-net over F8, using
- 1 times m-reduction [i] based on digital (113, 138, 21849)-net over F8, using
- net defined by OOA [i] based on linear OOA(8138, 21849, F8, 25, 25) (dual of [(21849, 25), 546087, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8138, 262189, F8, 25) (dual of [262189, 262051, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8138, 262191, F8, 25) (dual of [262191, 262053, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(891, 262144, F8, 18) (dual of [262144, 262053, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(811, 47, F8, 6) (dual of [47, 36, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(8138, 262191, F8, 25) (dual of [262191, 262053, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8138, 262189, F8, 25) (dual of [262189, 262051, 26]-code), using
- net defined by OOA [i] based on linear OOA(8138, 21849, F8, 25, 25) (dual of [(21849, 25), 546087, 26]-NRT-code), using
(137−24, 137, 322588)-Net over F8 — Digital
Digital (113, 137, 322588)-net over F8, using
(137−24, 137, large)-Net in Base 8 — Upper bound on s
There is no (113, 137, large)-net in base 8, because
- 22 times m-reduction [i] would yield (113, 115, large)-net in base 8, but